![4. Consider the following system [ 1.2 1 0 1 x (k + 1) = 0.6 0 1 x (k) + | –0.8 0 0 y (k) = [ 5 +a 0 0 ]x (k) 0 1 | 0.8 u(k)](http://img.homeworklib.com/questions/09a11680-a22a-11ea-a072-f189377c4871.png?x-oss-process=image/resize,w_560)
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4. Consider the following system [ 1.2 1 0 1 x (k +...
1. Consider the system described by: *(t) - 6 m (0) + veu(t): y(t) = 01...
1. Consider the system described by: *(t) - 6 m (0) + veu(t): y(t) = 01 (1) 60 = {1, 1421 a) Find the state transition matrix and the impulse response matrix of the system. b) Determine whether the system is (i) completely state controllable, (ii) differentially control- lable, (iii) instantaneously controllable, (iv) stabilizable at time to = 0. c) Repeat part (b) for to = 1. d) Determine whether the system is (i) observable, (ii) differentially observable, (iii) instanta-...
b(t) 1. Consider the system described by: 2. Consider the sy uuu It tet i(t) =...
b(t) 1. Consider the system described by: 2. Consider the sy uuu It tet i(t) = 0 -1 ] y(t) = (1 out) u(t) , 0, \t <1 (1, t > 1 a) Find the state transition matrix and the impulse response matrix of the system. 2D) Determine whether the system is (i) completely state controllable, (ii) differentially control lable, (iii) instantaneously controllable, (iv) stabilizable at time to = 0. (c) Repeat part (b) for to = 1. gd) Determine...
3. Consider a system with the governing equation of motion: 4 0 0 0201 +1-1 2-1 |x=0 4- 0 L0 0 0 -1 Obtain the characteristic equation. Explain how to obtain the mode shapes. You do not need to actua...
3. Consider a system with the governing equation of motion: 4 0 0 0201 +1-1 2-1 |x=0 4- 0 L0 0 0 -1 Obtain the characteristic equation. Explain how to obtain the mode shapes. You do not need to actually compute the mode shapes
3. Consider a system with the governing equation of motion: 4 0 0 0201 +1-1 2-1 |x=0 4- 0 L0 0 0 -1 Obtain the characteristic equation. Explain how to obtain the mode shapes. You do...
The control system defined by Problem 4. x(k 1)1 X2(k +1)] に0.16-1]1X2(k)], 10.5 is completely s...
The control system defined by Problem 4. x(k 1)1 X2(k +1)] に0.16-1]1X2(k)], 10.5 is completely state controllable. Assuming that the initial condition is x2(0)L-1 Determine control signals u(0) and u(1) such that the state x (2) is x1(2)1I-1 [X2:1-1-11
The control system defined by Problem 4. x(k 1)1 X2(k +1)] に0.16-1]1X2(k)], 10.5 is completely state controllable. Assuming that the initial condition is x2(0)L-1 Determine control signals u(0) and u(1) such that the state x (2) is x1(2)1I-1 [X2:1-1-11
Problem 5 Consider the linear system [1 2 0 2 -4 7x(t) 1 -4 6 y(t)...
Problem 5 Consider the linear system [1 2 0 2 -4 7x(t) 1 -4 6 y(t) [1 -2 2] (t). (4) a(t = (a) Is the system (4) observable? (b) Give a basis for the unobservable subspace of the system (4). In the remainder of this problem, consider the linear system а — 3 8— 2а 0 1 2a u(t) (t) (5) x(t) = with a a real parameter. (c) Determine all values of a for which the system (5)...
11 Q-Consider the discrete tim system 1-1 x(k+1)= 1-5 1-2 0 1 0 11 3 x(k)...
11 Q-Consider the discrete tim system 1-1 x(k+1)= 1-5 1-2 0 1 0 11 3 x(k) + 1 2 u(k), y(k)= (-3 1 1] x(k) NW 0 Given u(O)=u(1)=0, y(O)=1 , y(1)=2 Find x(2), and x(0) if possible
4. (30%) Consider a 2-dof system with 8 -2 1 0 [m] = 0 4 [k]...
4. (30%) Consider a 2-dof system with 8 -2 1 0 [m] = 0 4 [k] = -2 2 (a) Find the natural frequencies and mode shapes of the system. (b) Find the uncoupled modal equations. (c) If the system has proportional damping and it is known that the damping ratios are both 0.05 for the 2 modes, find the damping matrix of the system.
with steps please 04. For the system shown in Figure 4 where m-10 kg, k-100 kN/m, the governing equations has been d...
with steps please
04. For the system shown in Figure 4 where m-10 kg, k-100 kN/m, the governing equations has been derived as (1) Find the natural frequencies of the system; (2) Determine the associated mode shapes; and (3) Obtain the vibration response if the initial conditions are given as x,(0)-0,x,(0)-0.001 m, 2kE TIITTTUITTU Figure 4
04. For the system shown in Figure 4 where m-10 kg, k-100 kN/m, the governing equations has been derived as (1) Find the natural...
1- Consider a state space representation defined by LTI system, show why the system can be...
1- Consider a state space representation defined by LTI system, show why the system can be stabilized whether or not by using the state feedback control u=-Kx, whatever K is chosen? 35p [*]-[:][:] [:)
x(0) = 0 Consider the system defined by * = AX + Bu Where 1 A...
x(0) = 0 Consider the system defined by * = AX + Bu Where 1 A = (-6-3) BEG 1 and u=C)=6:10 [2.1(t) (5.1(t). Obtain the response x(t) analytically.
1. Consider the system described by: *(t) - 6 m (0) + veu(t): y(t) = 01 (1) 60 = {1, 1421 a) Find the state transition matrix and the impulse response matrix of the system. b) Determine whether the system is (i) completely state controllable, (ii) differentially control- lable, (iii) instantaneously controllable, (iv) stabilizable at time to = 0. c) Repeat part (b) for to = 1. d) Determine whether the system is (i) observable, (ii) differentially observable, (iii) instanta-...
b(t) 1. Consider the system described by: 2. Consider the sy uuu It tet i(t) = 0 -1 ] y(t) = (1 out) u(t) , 0, \t <1 (1, t > 1 a) Find the state transition matrix and the impulse response matrix of the system. 2D) Determine whether the system is (i) completely state controllable, (ii) differentially control lable, (iii) instantaneously controllable, (iv) stabilizable at time to = 0. (c) Repeat part (b) for to = 1. gd) Determine...
3. Consider a system with the governing equation of motion: 4 0 0 0201 +1-1 2-1 |x=0 4- 0 L0 0 0 -1 Obtain the characteristic equation. Explain how to obtain the mode shapes. You do not need to actually compute the mode shapes
3. Consider a system with the governing equation of motion: 4 0 0 0201 +1-1 2-1 |x=0 4- 0 L0 0 0 -1 Obtain the characteristic equation. Explain how to obtain the mode shapes. You do...
The control system defined by Problem 4. x(k 1)1 X2(k +1)] に0.16-1]1X2(k)], 10.5 is completely state controllable. Assuming that the initial condition is x2(0)L-1 Determine control signals u(0) and u(1) such that the state x (2) is x1(2)1I-1 [X2:1-1-11
The control system defined by Problem 4. x(k 1)1 X2(k +1)] に0.16-1]1X2(k)], 10.5 is completely state controllable. Assuming that the initial condition is x2(0)L-1 Determine control signals u(0) and u(1) such that the state x (2) is x1(2)1I-1 [X2:1-1-11
Problem 5 Consider the linear system [1 2 0 2 -4 7x(t) 1 -4 6 y(t) [1 -2 2] (t). (4) a(t = (a) Is the system (4) observable? (b) Give a basis for the unobservable subspace of the system (4). In the remainder of this problem, consider the linear system а — 3 8— 2а 0 1 2a u(t) (t) (5) x(t) = with a a real parameter. (c) Determine all values of a for which the system (5)...
11 Q-Consider the discrete tim system 1-1 x(k+1)= 1-5 1-2 0 1 0 11 3 x(k) + 1 2 u(k), y(k)= (-3 1 1] x(k) NW 0 Given u(O)=u(1)=0, y(O)=1 , y(1)=2 Find x(2), and x(0) if possible
4. (30%) Consider a 2-dof system with 8 -2 1 0 [m] = 0 4 [k] = -2 2 (a) Find the natural frequencies and mode shapes of the system. (b) Find the uncoupled modal equations. (c) If the system has proportional damping and it is known that the damping ratios are both 0.05 for the 2 modes, find the damping matrix of the system.
with steps please
04. For the system shown in Figure 4 where m-10 kg, k-100 kN/m, the governing equations has been derived as (1) Find the natural frequencies of the system; (2) Determine the associated mode shapes; and (3) Obtain the vibration response if the initial conditions are given as x,(0)-0,x,(0)-0.001 m, 2kE TIITTTUITTU Figure 4
04. For the system shown in Figure 4 where m-10 kg, k-100 kN/m, the governing equations has been derived as (1) Find the natural...
1- Consider a state space representation defined by LTI system, show why the system can be stabilized whether or not by using the state feedback control u=-Kx, whatever K is chosen? 35p [*]-[:][:] [:)
x(0) = 0 Consider the system defined by * = AX + Bu Where 1 A = (-6-3) BEG 1 and u=C)=6:10 [2.1(t) (5.1(t). Obtain the response x(t) analytically.
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